Past Problems of the Week

9/14: Compute the number of distinct 11 letter palindromic permutations of the letters of MISSISSIPPI.​9/21:In acute-angled triangle ABC, m<A = (x+15)°, m<B = (2x-6)°, and the exterior angle at C has measure (3x+9)°. Compute the number of possible integral values of x.

9/28: Relay!: ​Set #2 P1. Square ABCD is inscribed in a circle. Square EFGH has vertices E and F on CD and vertices G and H on the circle. Find the ratio of the area of square ABCD to the area of square EFGH.

Set #2 P2. Let T = TNYWR. Find the number of 0s at the right end of the decimal representation of 1!2!3!4!...(T-1)!T!

10/12: How many integers n with 10 ≤ n ≤ 500 have the property that the hundreds digit of 17n and 17n+ 17 are different?

​10/19: In isosceles triangle ABC with base BC of length 23 cm, points P and Q are chosen on side BC with BP = QC = 9 cm. If segments AP and AQ trisect angle BAC, what is the perimeter of triangle ABC?

​10/26: Define an increasing sequence a1, a2, a3, ..., ak of integers to be n-true if it satisfies the following conditions for positive integers n and k:i) The difference between any two consecutive terms is less than n.ii) The sequence must start with 0 and end with 10. How many 5-true sequences exist?

​11/2:Find the sum of all integers y on the interval 0 < y < 100 such that for some positive integer x, (x+sqrt(y)) + 1/(x+sqrt(y)) is an integer.

​11/9:In rectangle ABCD, AB = 2016 and BC = 1. Points E and F lie on segment AB such that BE = 2BF. The midpoints of EC and FD are M and N, respectively. If MN = 1000, what is the area of quadrilateral ENMB?

​11/16:How many ways can we pick four 3-element subsets of {1, 2, ..., 6} so that each pair of subsets share exactly one element?

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